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+uCa+Hereisageneralguide:uInverseTrigFunction(sin,arccos,xxetc)LogarithmicFunctions(log3,ln(1),xxetc)AlgebraicFunctions(xxx3,5,1/,etc)This chapterisabouttheideaofintegration,andalsoaboutthetechniqueofintegration.+.Weexplainhowitisdoneinprinciple,andthenhowitisdoneinpractice. Methodofsubstitution+∫xdxIntegrationisaproblemofaddingupinfinitelymanythings,eachofwhichisinfinitesimallysmallIntegrationbypartspThelistof basicintegralformulasisgivenbelow:∫dx=x+C∫adx=ax+C∫xndx=((xn+1)/(n+1))+C;n≠∫sinxdx=–cosx+C∫cosxdx=sinx+C∫secxdx= tanx+CBasicintegrationformulaskdx=kx+C(anynumberk)tan(x)dx=ln|sec(x)|+Cxndx=xn+n++C(n6= 1)cot(x)dx=ln|sin(x)|+Cxdx=ln|x|+Csec(x)dx= ln|sec(x)+tan(x)|+Cexdx=ex+Ccsc(x)dx= ln|csc(x)+cot(x)|+Caxdx=ln(a)+C(a>0,a6=1)sinh(x)dx=cosh(x)+Csin(x)dx= cos(x)+Ccosh(x)dx=sinh(x) +CIntegrationFormulas:(1)Zxpdx=xp+1p+1+C;p6=(2)Zsin(x)dx=cos(x)+C(3)Zcos(x)dx=sin(x)+C(4)Zsec2(x)dx=tan(x)+C(5)Zcsc2(x)dx= cot(x)+C(6)Zsec(x)tan(x)dx=sec(x)+C(7)Zcsc(x)cot(x)dx=csc(x)+C(8)Zxdx=lnjxj+C(9)Ztan(x)dx=lnjcos(x)j+C=lnjsec(x)j+C(10)Zsec(x)dx =lnjsec(x)+tan(x)j+C(11)ZIntegrationbyParts:Knowingwhichfunctiontocalluandwhichtocalldvtakessomepractice.ClickHeretoDownload INTEGRATIONFORMULAEPDFIntegrationFormulasforClassStudents∫IndefiniteIntegralTheStandardIntegralsListofIntegralFormulasAbstractZ duWehavetodistinguishtwodifferentkindsofintegrals=+C+∫dx=lnx+CxCa2uZIntegralsofRationalandIrrationalFunctionsThedefiniteone involvesthelimitsand4,theindefiniteonedoesn't:Theindefiniteintegralisafunctionf(x)=4x-ixThedefiniteintegralfromx=tox=isthenumberf(4)-f(0)duu DoingtheadditionisnotrecommendedIntegrationFormulassec(x)|+Cxndx=xn+n++C(n6= 1)cot(x)dx=ln|sin(x)|+Cxdx= = √ ∫ = ∫sin( ) =cos( )∫cos( ) =sin( )TrigonometricIntegrals:∫sec2( ) =tan( )∫csc2( ) =cot( )∫ MITMathematics, Useful IdentitiesTrigonometricIdentitiesHyperbolicIdentitiesComplexRelationshipsConstants,BinomialCoefficientsandthex|+C(3)Zexdx=ex+C(4)Zaxdx=lna ax+C(5)Zlnxdx=xlnxx+C(6)Zsinxdx7, Here,fundamentalintegrationformulasforvariousfunctionsarementioned∫f(x)g′(x)dx=f(x)g(x) ∫g(x)f ′(x)dxTheybothusetheantiderivativef(x)nxnInadditiontothefundamentalintegrationformulas,thisarticlealsoprovidesa, IntegrationFormulasPDF Download∫f(g(x))g′(x)dx=∫f(u)du=arctanuaIntegralFormulasforDifferentFunctionsZdu=arcsinInthissectionweshalldealwithsome techniquesofintegration,regardedasIntegrationFormulasCommonIntegralsBrianKnightPhD&RogerAdamsMScChapterAccessesPracticeProblemsc dx=cx+CxIntegralFormulasPDFClassificationofIntegralFormulas